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" If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles... "
Euclid's Elements of geometry, books i. ii. iii. iv - Seite 4
von Euclides - 1862
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The Mystery of Space: A Study of the Hyperspace Movement in the Light of the ...

Robert T. Browne - 1919 - 395 Seiten
...mankind. The parallel-postulate, as stated by EUCLID in his Elements of Geometry, reads as follows: "If a straight line meet two straight lines so as...lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles." On this postulate hang...
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Solid Geometry

Charles Austin Hobbs - 1921 - 192 Seiten
...corresponding angles equal, the two lines are parallel. Prop. 41. If two lines are cut by a transversal so as to make the two interior angles on the same side of the transversal supplementary, the lines are parallel. Prop. 41, Cor. II. Two lines respectively perpendicular...
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Tufts College Graduate, Bände 1-2

1901
...far from "self-evident" it is the reader may judge for himself. "If a straight line meets two other straight lines so as to make the two interior angles...it taken together less than two right angles, these sides being continually produced shall at length meet on that side on which are the angles which are...
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Transactions of the Royal Society of New Zealand, Band 18

1886
...of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is: — "If a straight line meets two straight lines, so as to make the two interior...lines being continually produced shall at length meet upon that side on which are the angles which are less than two right angles." In other words, if the...
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - 1955 - 389 Seiten
...parallels cut hy a transversal make equal alternate angles, he hrings m the unwieldly postulate or axiom: " If a straight line meet two straight lines, so as...less than two right angles, these straight lines, heing continually produced, shall at length meet on that side on which are the angles which are less...
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George Boole: Selected Manuscripts on Logic and its Philosophy

Ivor Grattan-Guinness, Gerard Bornet - 1997 - 236 Seiten
...4. And that all right angles are equal to one another. 5. And that if a straight line meet two other straight lines so as to make the two interior angles...these straight lines being continually produced shall meet on that side on which are the angles which are less than two right angles. 6. And that two straight...
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Transactions and Proceedings of the New Zealand Institute, Band 18

New Zealand Institute - 1886
...the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is : — " If a straight line meets two straight lines, so as to make the two interior...than two right angles, these straight lines being I continually produced shall at length meet upon that side on which are the angles which are less than...
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New Monthly Magazine, Band 30

Thomas Campbell, Samuel Carter Hall, Edward Bulwer Lytton Baron Lytton, Theodore Edward Hook, Thomas Hood, William Harrison Ainsworth - 1830
...FRS, of which we give the following extract : — The axiom states, that " if a straight line meets two straight lines, so as to make the two interior...taken together, less than two right angles, these two straight lines, being continually produced, shall, at length, meet upon that side on which are...
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A Short Hstory of of Greek Mathematics

James Gow
...which the last three are 10. Two straight lines cannot enclose a space: 11. All right angles are equal: 12. If a straight line meet two straight lines, so...make the two interior angles on the same side of it together less than two right angles, these straight lines will meet if produced on that side. Of these...
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The American Mathematical Monthly: Devoted to the Interests of ..., Bände 3-4

1896
...former we have the sum of the two angles AKH and CfJK equal to two right angles. QED PROPOSITION XI. If a straight line meet two straight lines so as to...the two interior angles on the same side of it taken tdgethcr less than two light angles, these straight lines, being continually produced, shall at length...
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